The campaign group issued a statement after it was confirmed that both the FA and Nicolas Anelka would not appeal against the five-match suspension handed to the West Brom striker for his 'quenelle' goal celebration.
Anelka performed the controversial salute after scoring against West Ham in December and was subsequently found guilty of an "aggravated breach of FA Rule E3" which relates to "ethnic origin and/or race and/or religion or belief".
An Independent Regulatory Board determined the length of Anelka's suspension, with the FA having pushed for a longer ban.
In their statement, Kick It Out also suggested that Anelka should have been handed a longer sanction and expressed frustration at the FA's decision not to appeal.
The statement read: "Kick It Out notes the decisions made by The Football Association (FA) and Nicolas Anelka not to appeal the Independent Regulatory Commission's outcome.
"Kick It Out finds it difficult to reconcile the sanctions imposed and conclusions reached by the commission, as set out in its written reasons, having regard to the evidence heard and issued in its report.
"The FA provided a hard body of evidence, complimented by in-depth research into the quenelle by an appointed expert, to justify a stronger ban than its five-match minimum.
"Kick It Out acknowledges The FA's explanation for not appealing the decision yet people will be perplexed as to why it has not been challenged considering they were clearly seeking a sanction which was quite different.
"Kick It Out urges The FA to review its anti-discrimination regulations and increase its minimum ban for players found guilty of discriminatory acts to 10 matches, in line with UEFA, so as to provide a much more meaningful deterrent to deal with potential offences."
West Brom issued Anelka with a club suspension after his initial ban was enforced, a move that has also prompted criticism from Kick It Out, who feel swifter action was required.
"Clubs should demonstrate their leadership obligations and community responsibility by taking action themselves against any of their employees including footballers who have breached disciplinary codes," they added.
"In the case of footballers, they should not automatically defend their actions and leave it to the The FA to deal with the matter.
"It was clear from the outset of this incident that Anelka's conduct caused great offence to many people, both within the Jewish community and the wider public.
"His employer West Bromwich Albion should have exercised its leadership as a community institution to apologise for the offence caused and deal with the matter in accordance with its disciplinary procedures.
"Clubs have a duty to their staff, their fans and the wider public. Kick It Out hopes that West Bromwich Albion would make every effort in future to take action that reinforces its commitment to tackle discriminatory, unjust and prejudiced behaviour, thereby seeking to re-establish its previously good reputation in tackling such matters.
"Kick It Out calls on The FA, the Premier League and Football League to ensure that all football clubs within their jurisdiction have policies and procedures which require them to deal with all misconduct matters in line with best employment practice."
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